A254711 Pentagonal numbers (A000326) which are also centered square numbers (A001844).

1, 5, 145, 925, 28085, 179401, 5448301, 34802825, 1056942265, 6751568605, 205041351065, 1309769506501, 39776965164301, 254088532692545, 7716526200523285, 49291865572847185, 1496966305936352945, 9562367832599661301, 290403746825451948001

Offset

1,2

Links

Colin Barker, Table of n, a(n) for n = 1..875

Index entries for linear recurrences with constant coefficients, signature (1,194,-194,-1,1).

Formula

a(n) = a(n-1)+194*a(n-2)-194*a(n-3)-a(n-4)+a(n-5).

G.f.: -x*(x^4+4*x^3-54*x^2+4*x+1) / ((x-1)*(x^2-14*x+1)*(x^2+14*x+1)).

Example

145 is in the sequence because it is the 10th pentagonal number and the 9th centered square number.

Prog

(PARI) Vec(-x*(x^4+4*x^3-54*x^2+4*x+1)/((x-1)*(x^2-14*x+1)*(x^2+14*x+1)) + O(x^100))

Crossrefs

Cf. A000326, A001844, A254709, A254710.

Sequence in context: A081322 A232986 A322954 * A273920 A076218 A267989

Adjacent sequences: A254708 A254709 A254710 * A254712 A254713 A254714

Keyword

nonn,easy

Author

Colin Barker, Feb 06 2015

Status

approved