A135526 Number of sums payable using exactly n banknotes of denominations 1, 5, 10, 20, 50, 100 (change allowable).

1, 6, 33, 95, 188, 288, 388, 488, 588, 688, 788, 888, 988, 1088, 1188, 1288, 1388, 1488, 1588, 1688, 1788, 1888, 1988, 2088, 2188, 2288, 2388, 2488, 2588, 2688, 2788, 2888, 2988, 3088, 3188, 3288, 3388, 3488, 3588, 3688, 3788, 3888, 3988, 4088, 4188, 4288

Offset: 0

Author

Zak Seidov, Feb 20 2008

Keywords

• nonn
• easy

Comments

Terms and formula from Max Alekseyev and Robert Israel.

Links

• G. C. Greubel, Table of n, a(n) for n = 0..1000
• Index entries for linear recurrences with constant coefficients, signature (2,-1).

Crossrefs

Cf. A124146, A135137, A135454.

Programs

Mathematica

Join[{1,6,33,95}, LinearRecurrence[{2,-1},{188,288},25]] (* or *) Join[{1,6,33,95}, Table[100*n -212, {n,4,25}]] (* G. C. Greubel, Oct 17 2016 *)

PARI

a(n)=if(n>3,100*n-212,[1,6,33,95][n+1]) \\ Charles R Greathouse IV, Jun 23 2024

Formula

a(n) = 100*n - 212 for n>=4.

From G. C. Greubel, Oct 17 2016: (Start)

a(n) = 2*a(n-1) - a(n-2), for n >= 4.

G.f.: (1 + 4*x + 22*x^2 + 35*x^3 + 31*x^4 + 7*x^5)/(1-x)^2.

E.g.f.: (1/6)*( 1278 + 708*x + 135*x^2 + 7*x^3 - 24*(53 - 25*x)*exp(x) ). (End)

Extensions

Extended by Max Alekseyev, Mar 04 2009