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A253477 Indices of centered heptagonal numbers (A069099) which are also centered triangular numbers (A005448). 3
1, 10, 46, 1045, 5005, 114886, 550450, 12636361, 60544441, 1389884770, 6659338006, 152874688285, 732466636165, 16814825826526, 80564670640090, 1849477966229521, 8861381303773681, 203425761459420730, 974671378744464766, 22374984282570050725 (list; graph; refs; listen; history; text; internal format)
OFFSET
1,2
COMMENTS
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.
LINKS
FORMULA
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)).
EXAMPLE
10 is in the sequence because the 10th centered heptagonal number is 316, which is also the 15th centered triangular number.
MATHEMATICA
LinearRecurrence[{1, 110, -110, -1, 1}, {1, 10, 46, 1045, 5005}, 30] (* Harvey P. Dale, Aug 13 2018 *)
PROG
(PARI) Vec(-x*(x^4+9*x^3-74*x^2+9*x+1)/((x-1)*(x^4-110*x^2+1)) + O(x^100))
CROSSREFS
Sequence in context: A219597 A000832 A242462 * A143895 A281767 A323799
KEYWORD
nonn,easy
AUTHOR
Colin Barker, Jan 02 2015
STATUS
approved

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Last modified July 12 08:07 EDT 2024. Contains 374239 sequences. (Running on oeis4.)