A098924 45-gonal numbers: n*(43*n-41)/2.

1, 45, 132, 262, 435, 651, 910, 1212, 1557, 1945, 2376, 2850, 3367, 3927, 4530, 5176, 5865, 6597, 7372, 8190, 9051, 9955, 10902, 11892, 12925, 14001, 15120, 16282, 17487, 18735, 20026, 21360, 22737, 24157, 25620, 27126, 28675, 30267

Offset: 1

Author

Parthasarathy Nambi, Oct 18 2004

Keywords

• nonn
• easy

Comments

Similar to 21-gonal and 15-gonal numbers (A051873, A051867).

Links

• Vincenzo Librandi, Table of n, a(n) for n = 1..1000
• Index to sequences related to polygonal numbers
• Index entries for linear recurrences with constant coefficients, signature (3,-3,1).

Crossrefs

Cf. A051867, A051873.

Programs

Magma

[n*(43*n-41)/2: n in [1..50]]; // Vincenzo Librandi, Jul 08 2012

Mathematica

Table[n(43n - 41)/2, {n, 1, 40}] (* Stefan Steinerberger, Feb 15 2006 *)
CoefficientList[Series[(1+42*x)/(1-x)^3,{x,0,50}],x] (* Vincenzo Librandi, Jul 08 2012 *)
LinearRecurrence[{3,-3,1},{1,45,132},40] (* Harvey P. Dale, Jan 24 2015 *)

PARI

a(n)=n*(43*n-41)/2 \\ Charles R Greathouse IV, Oct 16 2015

Formula

a(n) = n*(43*n-41)/2.

G.f.: x*(1+42*x)/(1-x)^3. - Bruno Berselli, Feb 04 2011

a(n) = 3*a(n-1) -3*a(n-2) +a(n-3). - Vincenzo Librandi, Jul 08 2012

E.g.f.: exp(x)*(x + 43*x^2/2). - Nikolaos Pantelidis, Feb 10 2023

Extensions

More terms from Stefan Steinerberger, Feb 15 2006