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A276915
Indices of triangular numbers in A276914 which are also pentagonal.
3
0, 1, 10, 143, 1988, 27693, 385710, 5372251, 74825800, 1042188953, 14515819538, 202179284583, 2815994164620, 39221739020101, 546288352116790, 7608815190614963, 105977124316492688, 1476070925240282673, 20559015829047464730, 286350150681424223551
OFFSET
0,3
COMMENTS
A276914(a(n)) = A014979(n + 1). All numbers which are both triangular and pentagonal can be found in sequence A276914.
FORMULA
a(n) = 14*a(n-1) - a(n-2) - 4*(-1)^n for n>1, a(0)=0, a(1)=1.
a(n) = (A046175(n) + (A046175(n) mod 2))/2.
From Colin Barker, Sep 23 2016: (Start)
G.f.: x*(1 - 3*x) / ((1 + x)*(1 - 14*x + x^2)).
a(n) = 13*a(n-1) + 13*a(n-2) - a(n-3) for n>2.
a(n) = ( -6*(-1)^n + (3+sqrt(3))*(7-4*sqrt(3))^n - (-3+sqrt(3))*(7+4*sqrt(3))^n )/24. (End)
MATHEMATICA
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 *)
PROG
(PARI) concat(0, Vec(x*(1-3*x)/((1+x)*(1-14*x+x^2)) + O(x^30))) \\ Colin Barker, Sep 23 2016
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
STATUS
approved