A135454 -id:A135454 - cp's OEIS frontend

A135137 Numbers that are the sum of three numbers from the set {1, 5, 10, 20, 50, 100}.

3, 7, 11, 12, 15, 16, 20, 21, 22, 25, 26, 30, 31, 35, 40, 41, 45, 50, 52, 56, 60, 61, 65, 70, 71, 75, 80, 90, 101, 102, 105, 106, 110, 111, 115, 120, 121, 125, 130, 140, 150, 151, 155, 160, 170, 200, 201, 205, 210, 220, 250, 300

Offset: 1

Julie Jones, Feb 13 2008

			sum, n1..n6 (from _Zak Seidov_):
3, 3,0,0,0,0,0,
7, 2,1,0,0,0,0,
11, 1,2,0,0,0,0,
12, 2,0,1,0,0,0,
15, 0,3,0,0,0,0,
16, 1,1,1,0,0,0,
20, 0,2,1,0,0,0,
21, 1,0,2,0,0,0,
22, 2,0,0,1,0,0,
25, 0,1,2,0,0,0,
...

Cf. A124146, A135454.

Union[Total/@Tuples[{1,5,10,20,50,100},{3}]] (* Harvey P. Dale, Jan 11 2011 *)

Edited by N. J. A. Sloane, Feb 18 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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A135137 Numbers that are the sum of three numbers from the set {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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