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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
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
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
KEYWORD
nonn,easy
AUTHOR
David W. Wilson, Jul 09 2002
STATUS
approved