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A254228 Indices of heptagonal numbers (A000566) which are also centered square numbers (A001844). 3
1, 41, 185, 13105, 59473, 4219673, 19150025, 1358721505, 6166248481, 437504104841, 1985512860761, 140874963037201, 639328974916465, 45361300593873785, 205861944410240873, 14606197916264321473, 66286906771122644545, 4703150367736517640425 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,2

COMMENTS

Also positive integers x in the solutions to 5*x^2 - 4*y^2 - 3*x + 4*y - 2 = 0, the corresponding values of y being A254229.

LINKS

Colin Barker, Table of n, a(n) for n = 1..797

Index entries for linear recurrences with constant coefficients, signature (1,322,-322,-1,1).

FORMULA

a(n) = a(n-1)+322*a(n-2)-322*a(n-3)-a(n-4)+a(n-5).

G.f.: -x*(x^4+40*x^3-178*x^2+40*x+1) / ((x-1)*(x^2-18*x+1)*(x^2+18*x+1)).

EXAMPLE

41 is in the sequence because the 41st heptagonal number is 4141, which is also the 46th centered square number.

PROG

(PARI) Vec(-x*(x^4+40*x^3-178*x^2+40*x+1)/((x-1)*(x^2-18*x+1)*(x^2+18*x+1)) + O(x^100))

CROSSREFS

Cf. A000566, A001844, A254229, A254230.

Sequence in context: A282941 A141922 A142080 * A141939 A264653 A297227

Adjacent sequences:  A254225 A254226 A254227 * A254229 A254230 A254231

KEYWORD

nonn,easy

AUTHOR

Colin Barker, Jan 27 2015

STATUS

approved

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Last modified July 31 10:51 EDT 2021. Contains 346373 sequences. (Running on oeis4.)