A068009 -id:A068009 - cp's OEIS frontend

A068041 Number of subsets of {1,2,3,...,n} that sum to 0 mod 20.

1, 1, 1, 1, 1, 1, 2, 6, 14, 26, 52, 103, 205, 410, 820, 1640, 3278, 6554, 13108, 26216, 52432, 104860, 209716, 419432, 838864, 1677728, 3355448, 6710888, 13421776, 26843552, 53687104, 107374192, 214748368, 429496736, 858993472, 1717986944

Offset: 0

Antti Karttunen, Feb 11 2002

nonn

20th row of A068009.

Empirical G.f.: (x-1)^2*(4*x^12+4*x^11-x^10-7*x^9-11*x^8-15*x^7-15*x^6-11*x^5-5*x^4-2*x^3+x+1) / ((2*x-1)*(2*x^5-1)). [Colin Barker, Dec 22 2012]

A068042 Number of subsets of {1,2,3,...,n} that sum to 0 mod 21.

Original entry on oeis.org

1, 1, 1, 1, 1, 1, 2, 6, 14, 26, 49, 99, 197, 391, 782, 1564, 3123, 6244, 12490, 24970, 49940, 99880, 199738, 399472, 798940, 1597844, 3195684, 6391368, 12782668, 25565336, 51130664, 102261174, 204522354, 409044702, 818089110, 1636178220

Offset: 0

Antti Karttunen, Feb 11 2002

nonn

21st row of A068009.

Empirical G.f.: -(8*x^31 -8*x^28 +4*x^27 -2*x^26 -2*x^25 -6*x^24 +4*x^23 +4*x^22 +2*x^21 +2*x^20 +6*x^19 -8*x^18 -12*x^17 -5*x^16 +6*x^15 +10*x^14 +x^13 -x^12 +5*x^11 +x^10 -6*x^8 -2*x^7 -2*x^6 -x^5 -x^4 +3*x^3 +x^2 +x -1) / ((2*x -1)*(2*x^3 -1)*(2*x^7 -1)*(2*x^21 -1)). [Colin Barker, Dec 22 2012]

A068043 Number of subsets of {1,2,3,...,n} that sum to 0 mod 25.

Original entry on oeis.org

1, 1, 1, 1, 1, 1, 1, 3, 10, 23, 43, 82, 164, 328, 656, 1312, 2622, 5243, 10486, 20972, 41945, 83887, 167773, 335546, 671092, 1342184, 2684360, 5368712, 10737422, 21474842, 42949682, 85899350, 171798690, 343597388, 687194782, 1374389558

Offset: 0

Antti Karttunen, Feb 11 2002

nonn

25th row of A068009.

Empirical G.f.: -(x -1) * (4*x^29 +4*x^28 +4*x^27 -4*x^24 -4*x^23 -4*x^22 -3*x^21 -2*x^20 -x^19 -x^18 -x^17 -2*x^16 +4*x^15 +10*x^14 +4*x^13 -4*x^12 -6*x^11 -8*x^10 -9*x^9 -4*x^8 +2*x^7 +5*x^6 +6*x^5 +3*x^4 +2*x^3 +x^2 -1) / ((2*x -1)*(2*x^5 -1)*(2*x^25 -1)). [Colin Barker, Dec 23 2012]

A068044 Number of subsets of {1,2,3,...,n} that sum to 0 mod 32.

Original entry on oeis.org

1, 1, 1, 1, 1, 1, 1, 1, 3, 14, 37, 71, 129, 253, 511, 1024, 2048, 4096, 8192, 16384, 32768, 65536, 131072, 262144, 524288, 1048576, 2097152, 4194304, 8388608, 16777216, 33554432, 67108864, 134217728, 268435456, 536870912, 1073741824

Offset: 0

Antti Karttunen, Feb 11 2002

Index entries for linear recurrences with constant coefficients, signature (2).

32nd row of A068009.

G.f.: -(2*x^15+5*x^14-5*x^13-13*x^12-3*x^11+9*x^10+8*x^9+x^8-x^7-x^6-x^5-x^4-x^3-x^2-x+1) / (2*x-1). Colin Barker, Dec 23 2012

cp's OEIS Frontend

A068041 Number of subsets of {1,2,3,...,n} that sum to 0 mod 20.

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A068042 Number of subsets of {1,2,3,...,n} that sum to 0 mod 21.

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A068043 Number of subsets of {1,2,3,...,n} that sum to 0 mod 25.

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A068044 Number of subsets of {1,2,3,...,n} that sum to 0 mod 32.

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