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A072277 Smallest integer > 1 which is both n-gonal and centered n-gonal. 1
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 (list; graph; refs; listen; history; text; internal format)
OFFSET

3,1

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

G.f.: x^3*(-3*x^3+11*x^2-15*x+10)/(x-1)^4 [From 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

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

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Last modified August 20 22:45 EDT 2019. Contains 326155 sequences. (Running on oeis4.)