A253459 Indices of centered square numbers (A001844) which are also centered heptagonal numbers (A069099).

1, 21, 148, 5208, 37465, 1322685, 9515836, 335956656, 2416984753, 85331667813, 613904611300, 21673907667720, 155929354285321, 5505087215932941, 39605442083860108, 1398270478939299168, 10059626359946181985, 355155196563366055605, 2555105489984246363956

Offset

1,2

Comments

Also positive integers x in the solutions to 4*x^2 - 7*y^2 - 4*x + 7*y = 0, the corresponding values of y being A253460.

Links

Colin Barker, Table of n, a(n) for n = 1..832

Index entries for linear recurrences with constant coefficients, signature (1,254,-254,-1,1).

Formula

a(n) = a(n-1)+254*a(n-2)-254*a(n-3)-a(n-4)+a(n-5).

G.f.: x*(20*x^3+127*x^2-20*x-1) / ((x-1)*(x^2-16*x+1)*(x^2+16*x+1)).

Example

21 is in the sequence because the 21st centered square number is 841, which is also the 16th centered heptagonal number.

Prog

(PARI) Vec(x*(20*x^3+127*x^2-20*x-1)/((x-1)*(x^2-16*x+1)*(x^2+16*x+1)) + O(x^100))

Crossrefs

Cf. A001844, A069099, A253460, A253599.

Sequence in context: A060493 A198183 A259493 * A041850 A239123 A241697

Adjacent sequences: A253456 A253457 A253458 * A253460 A253461 A253462

Keyword

nonn,easy

Author

Colin Barker, Jan 01 2015

Status

approved