A253599 -id:A253599 - cp's OEIS frontend

A253460 Indices of centered heptagonal numbers (A069099) which are also centered square numbers (A001844).

1, 16, 112, 3937, 28321, 999856, 7193296, 253959361, 1827068737, 64504677712, 464068265776, 16383934179361, 117871512438241, 4161454776879856, 29938900091047312, 1056993129393303937, 7604362751613578881, 268472093411122320016, 1931478200009757988336

Offset: 1

Colin Barker, Jan 01 2015

Also positive integers y in the solutions to 4*x^2 - 7*y^2 - 4*x + 7*y = 0, the corresponding values of x being A253459.

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

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).

Cf. A001844, A069099, A253459, A253599.

Vec(-x*(x^4+15*x^3-158*x^2+15*x+1)/((x-1)*(x^2-16*x+1)*(x^2+16*x+1)) + O(x^100))

a(n) = a(n-1)+254*a(n-2)-254*a(n-3)-a(n-4)+a(n-5).
G.f.: -x*(x^4+15*x^3-158*x^2+15*x+1) / ((x-1)*(x^2-16*x+1)*(x^2+16*x+1)).
a(n) = A105040(n) + 1. - Michel Marcus, Mar 12 2024

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

Original entry on oeis.org

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

Offset: 1

Colin Barker, Jan 01 2015

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.

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

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).

Cf. A001844, A069099, A253460, A253599.

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))

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)).

cp's OEIS Frontend

A253460 Indices of centered heptagonal numbers (A069099) which are also centered square numbers (A001844).

Views

Author

Keywords

Comments

Examples

Links

Crossrefs

Programs

PARI

Formula