cp's OEIS Frontend

This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.

A276915 Indices of triangular numbers in A276914 which are also pentagonal.

This page as a plain text file.
%I A276915 #23 Dec 17 2016 10:41:40
%S A276915 0,1,10,143,1988,27693,385710,5372251,74825800,1042188953,14515819538,
%T A276915 202179284583,2815994164620,39221739020101,546288352116790,
%U A276915 7608815190614963,105977124316492688,1476070925240282673,20559015829047464730,286350150681424223551
%N A276915 Indices of triangular numbers in A276914 which are also pentagonal.
%C A276915 A276914(a(n)) = A014979(n + 1). All numbers which are both triangular and pentagonal can be found in sequence A276914.
%H A276915 Daniel Poveda Parrilla, <a href="/A276915/b276915.txt">Table of n, a(n) for n = 0..200</a>
%H A276915 <a href="/index/Rec#order_03">Index entries for linear recurrences with constant coefficients</a>, signature (13,13,-1).
%F A276915 a(n) = 14*a(n-1) - a(n-2) - 4*(-1)^n for n>1, a(0)=0, a(1)=1.
%F A276915 a(n) = (A046175(n) + (A046175(n) mod 2))/2.
%F A276915 From _Colin Barker_, Sep 23 2016: (Start)
%F A276915 G.f.: x*(1 - 3*x) / ((1 + x)*(1 - 14*x + x^2)).
%F A276915 a(n) = 13*a(n-1) + 13*a(n-2) - a(n-3) for n>2.
%F A276915 a(n) = ( -6*(-1)^n + (3+sqrt(3))*(7-4*sqrt(3))^n - (-3+sqrt(3))*(7+4*sqrt(3))^n )/24. (End)
%t A276915 RecurrenceTable[{a[n] == 14 a[n - 1] - a[n - 2] - 4 (-1)^n, a[0] == 0, a[1] == 1}, a, {n, 19}] (* _Michael De Vlieger_, Sep 23 2016 *)
%o A276915 (PARI) concat(0, Vec(x*(1-3*x)/((1+x)*(1-14*x+x^2)) + O(x^30))) \\ _Colin Barker_, Sep 23 2016
%Y A276915 Cf. A014979, A046175, A276914.
%K A276915 nonn,easy
%O A276915 0,3
%A A276915 _Daniel Poveda Parrilla_, Sep 22 2016