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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
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.
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
KEYWORD
nonn,easy
AUTHOR
Colin Barker, Jan 27 2015
STATUS
approved