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

0,2

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).

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)

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 *)

Prog

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

Crossrefs

Cf. A124146, A135137, A135454.

Sequence in context: A157872 A153127 A274218 * A204185 A057818 A063267

Adjacent sequences: A135523 A135524 A135525 * A135527 A135528 A135529

Keyword

nonn,easy

Author

Zak Seidov, Feb 20 2008

Extensions

Extended by Max Alekseyev, Mar 04 2009

Status

approved