A329783 Numbers that are either +-2 (mod 5) or +-11 (mod 55).

2, 3, 7, 8, 11, 12, 13, 17, 18, 22, 23, 27, 28, 32, 33, 37, 38, 42, 43, 44, 47, 48, 52, 53, 57, 58, 62, 63, 66, 67, 68, 72, 73, 77, 78, 82, 83, 87, 88, 92, 93, 97, 98, 99, 102, 103, 107, 108, 112, 113, 117, 118, 121, 122, 123, 127, 128, 132, 133, 137, 138

Offset

1,1

Links

Table of n, a(n) for n=1..61.

G. E. Andrews, Further Problems on Partitions, The American Mathematical Monthly, Vol. 94, No. 5 (1987), 437-439.

Index entries for linear recurrences with constant coefficients, signature (1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, -1).

Formula

From Colin Barker, Dec 01 2019: (Start)

G.f.: x*(2 + x + 4*x^2 + x^3 + 3*x^4 + x^5 + x^6 + 4*x^7 + x^8 + 4*x^9 + x^10 + 4*x^11 + x^12 + 4*x^13 + x^14 + 4*x^15 + x^16 + 4*x^17 + x^18 + x^19 + 3*x^20 + x^21 + 4*x^22 + x^23 + 2*x^24) / ((1 - x)^2*(1 + x)*(1 - x + x^2)*(1 + x^2)*(1 + x + x^2)*(1 - x^2 + x^4)*(1 + x^4)*(1 - x^4 + x^8)).

a(n) = a(n-1) + a(n-24) - a(n-25) for n>25.

(End)

a(n) ~ 55*n/24. - Charles R Greathouse IV, May 21 2026

Prog

(PARI) a(n)=(n-1)\24*55+[53, 2, 3, 7, 8, 11, 12, 13, 17, 18, 22, 23, 27, 28, 32, 33, 37, 38, 42, 43, 44, 47, 48, 52][n%24+1] \\ Charles R Greathouse IV, May 21 2026

Crossrefs

Cf. A329779-A329784.

Sequence in context: A323003 A051468 A002274 * A287675 A273944 A214324

Adjacent sequences: A329780 A329781 A329782 * A329784 A329785 A329786

Keyword

nonn,easy

Author

N. J. A. Sloane, Nov 29 2019

Status

approved