A253622 Centered heptagonal numbers (A069099) which are also centered pentagonal numbers (A005891).
1, 106, 15016, 2132131, 302747551, 42988020076, 6103996103206, 866724458635141, 123068769130086781, 17474898492013687726, 2481312517096813570276, 352328902529255513291431, 50028222846637186073812891, 7103655315319951166968139056
Offset: 1
Examples
106 is in the sequence because it is the 6th centered heptagonal number and the 7th centered pentagonal number.
Links
- Colin Barker, Table of n, a(n) for n = 1..465
- Index entries for linear recurrences with constant coefficients, signature (143,-143,1).
Programs
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Mathematica
LinearRecurrence[{143,-143,1},{1,106,15016},20] (* Harvey P. Dale, Feb 25 2016 *) -
PARI
Vec(-x*(x^2-37*x+1)/((x-1)*(x^2-142*x+1)) + O(x^100))
Formula
a(n) = 143*a(n-1)-143*a(n-2)+a(n-3).
G.f.: -x*(x^2-37*x+1) / ((x-1)*(x^2-142*x+1)).
a(n) = (4+(6+sqrt(35))*(71+12*sqrt(35))^(-n)-(-6+sqrt(35))*(71+12*sqrt(35))^n)/16. - Colin Barker, Mar 07 2016