A253689 -id:A253689 - cp's OEIS frontend

A253476 Indices of centered triangular numbers (A005448) which are also centered heptagonal numbers (A069099).

1, 15, 70, 1596, 7645, 175491, 840826, 19302360, 92483161, 2123084055, 10172306830, 233519943636, 1118861268085, 25685070715851, 123064567182466, 2825124258799920, 13535983528803121, 310737983397275295, 1488835123601160790, 34178353049441482476

Offset: 1

Colin Barker, Jan 02 2015

Also positive integers x in the solutions to 3*x^2 - 7*y^2 - 3*x + 7*y = 0, the corresponding values of y being A253477.

			15 is in the sequence because the 15th centered triangular number is 316, which is also the 10th centered heptagonal number.

Colin Barker, Table of n, a(n) for n = 1..980
Index entries for linear recurrences with constant coefficients, signature (1,110,-110,-1,1).

Cf. A005448, A069099, A253477, A253689.

LinearRecurrence[{1,110,-110,-1,1},{1,15,70,1596,7645},30] (* Harvey P. Dale, Jun 14 2016 *)

Vec(x*(14*x^3+55*x^2-14*x-1)/((x-1)*(x^4-110*x^2+1)) + O(x^100))

a(n) = a(n-1)+110*a(n-2)-110*a(n-3)-a(n-4)+a(n-5).

G.f.: x*(14*x^3+55*x^2-14*x-1) / ((x-1)*(x^4-110*x^2+1)).

A253477 Indices of centered heptagonal numbers (A069099) which are also centered triangular numbers (A005448).

Original entry on oeis.org

1, 10, 46, 1045, 5005, 114886, 550450, 12636361, 60544441, 1389884770, 6659338006, 152874688285, 732466636165, 16814825826526, 80564670640090, 1849477966229521, 8861381303773681, 203425761459420730, 974671378744464766, 22374984282570050725

Offset: 1

Colin Barker, Jan 02 2015

Also positive integers y in the solutions to 3*x^2 - 7*y^2 - 3*x + 7*y = 0, the corresponding values of x being A253476.

			10 is in the sequence because the 10th centered heptagonal number is 316, which is also the 15th centered triangular number.

Colin Barker, Table of n, a(n) for n = 1..980
Index entries for linear recurrences with constant coefficients, signature (1,110,-110,-1,1).

Cf. A005448, A069099, A253476, A253689.

LinearRecurrence[{1,110,-110,-1,1},{1,10,46,1045,5005},30] (* Harvey P. Dale, Aug 13 2018 *)

Vec(-x*(x^4+9*x^3-74*x^2+9*x+1)/((x-1)*(x^4-110*x^2+1)) + O(x^100))

a(n) = a(n-1)+110*a(n-2)-110*a(n-3)-a(n-4)+a(n-5).

G.f.: -x*(x^4+9*x^3-74*x^2+9*x+1) / ((x-1)*(x^4-110*x^2+1)).

cp's OEIS Frontend

A253476 Indices of centered triangular numbers (A005448) which are also centered heptagonal numbers (A069099).

Views

Author

Keywords

Comments

Examples

Links

Crossrefs

Programs

Mathematica

PARI

Formula