OFFSET
0,3
COMMENTS
Also generalized tridecagonal numbers or generalized triskaidecagonal numbers.
Numbers k for which 88*k + 81 is a square. - Bruno Berselli, Jul 10 2018
LINKS
Vincenzo Librandi, Table of n, a(n) for n = 0..10000
Index entries for linear recurrences with constant coefficients, signature (1,2,-2,-1,1).
FORMULA
From Bruno Berselli, Sep 15 2011: (Start)
G.f.: x*(1 + 9*x + x^2)/((1 + x)^2*(1 - x)^3).
a(n) = (22*n*(n + 1) + 7*(2*n + 1)*(-1)^n - 7)/16.
a(n) - a(n-2) = A175885(n). (End)
Sum_{n>=1} 1/a(n) = 22/81 + 2*Pi*cot(2*Pi/11)/9. - Vaclav Kotesovec, Oct 05 2016
MAPLE
a:= n-> (m-> m*(11*m-9)/2)(-ceil(n/2)*(-1)^n):
seq(a(n), n=0..60); # Alois P. Heinz, Jul 10 2018
MATHEMATICA
lim = 50; Sort[Table[n*(11*n - 9)/2, {n, -lim, lim}]] (* T. D. Noe, Sep 15 2011 *)
Accumulate[With[{nn=30}, Riffle[9Range[0, nn], Range[1, 2nn+1, 2]]]] (* Harvey P. Dale, Sep 24 2011 *)
PROG
(Magma) [(22*n*(n+1)+7*(2*n+1)*(-1)^n-7)/16: n in [0..50]]; // Vincenzo Librandi, Sep 16 2011
(Magma) A195313:=func<n | n*(11*n-9)/2>; [0] cat [A195313(n*m): m in [1, -1], n in [1..25]]; // Bruno Berselli, Nov 13 2012
(PARI) a(n)=(22*n*(n+1)+7*(2*n+1)*(-1)^n-7)/16 \\ Charles R Greathouse IV, Sep 24 2015
CROSSREFS
Partial sums of A195312.
Column 9 of A195152.
Cf. A316672.
Sequences of generalized k-gonal numbers: A001318 (k=5), A000217 (k=6), A085787 (k=7), A001082 (k=8), A118277 (k=9), A074377 (k=10), A195160 (k=11), A195162 (k=12), this sequence (k=13), A195818 (k=14), A277082 (k=15), A274978 (k=16), A303305 (k=17), A274979 (k=18), A303813 (k=19), A218864 (k=20), A303298 (k=21), A303299 (k=22), A303303 (k=23), A303814 (k=24), A303304 (k=25), A316724 (k=26), A316725 (k=27), A303812 (k=28), A303815 (k=29), A316729 (k=30).
KEYWORD
nonn,easy
AUTHOR
Omar E. Pol, Sep 14 2011
STATUS
approved