A135137 -id:A135137 - cp's OEIS frontend

A135454 Number of sums payable using exactly n banknotes of denominations 1, 5, 10, 20, 50, 100.

1, 6, 21, 52, 103, 174, 262, 360, 461, 561, 660, 759, 858, 957, 1056, 1155, 1254, 1353, 1452, 1551, 1650, 1749, 1848, 1947, 2046, 2145, 2244, 2343, 2442, 2541, 2640, 2739, 2838, 2937, 3036, 3135, 3234, 3333, 3432, 3531, 3630, 3729, 3828

Offset: 0

Zak Seidov, Feb 16 2008

nonn

			n=1: 6 payable sums are 1,5,10,20,50,100;
n=3: the 52 sums are in A135137.

Corrected and extended by Joshua Zucker, Feb 16 2008

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

Original entry on oeis.org

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

Zak Seidov, Feb 20 2008

Terms and formula from Max Alekseyev and Robert Israel.

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

Cf. A124146, A135137, A135454.

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 *)

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

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)

Extended by Max Alekseyev, Mar 04 2009

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A135454 Number of sums payable using exactly n banknotes of denominations 1, 5, 10, 20, 50, 100.

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

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