A072277 Smallest integer > 1 which is both n-gonal and centered n-gonal.

10, 25, 51, 91, 148, 225, 325, 451, 606, 793, 1015, 1275, 1576, 1921, 2313, 2755, 3250, 3801, 4411, 5083, 5820, 6625, 7501, 8451, 9478, 10585, 11775, 13051, 14416, 15873, 17425, 19075, 20826, 22681, 24643, 26715, 28900, 31201, 33621, 36163

Offset

3,1

Comments

a(n) is the (n-1)-th centered n-gonal number. The n-th centered n-gonal number is A100119(n) and the (n+1)-th centered n-gonal number is A158842(n). - Mohammed Yaseen, Jun 06 2021

Links

Table of n, a(n) for n=3..42.

Index entries for linear recurrences with constant coefficients, signature (4,-6,4,-1).

Formula

a(n) = (n^3 - n^2 + 2)/2.

a(n) = 4*a(n-1) - 6*a(n-2) + 4*a(n-3) - a(n-4), with a(3)=10, a(4)=25, a(5)=51, a(6)=91. - Harvey P. Dale, Aug 19 2011

G.f.: x^3*(-3*x^3 + 11*x^2 - 15*x + 10)/(x-1)^4. - Harvey P. Dale, Aug 19 2011

Example

a(4) = 25 is both square and centered square.

Mathematica

LinearRecurrence[{4, -6, 4, -1}, {10, 25, 51, 91}, 50] (* or *) Table[(n^3-n^2+ 2)/2, {n, 3, 50}] (* Harvey P. Dale, Aug 19 2011 *)

Crossrefs

Cf. A100119, A158842, A162607.

Sequence in context: A024838 A020179 A022670 * A283243 A263310 A063424

Adjacent sequences: A072274 A072275 A072276 * A072278 A072279 A072280

Keyword

nonn,easy

Author

David W. Wilson, Jul 09 2002

Status

approved