A003403 G.f.: (1 + x^3 + x^4 + ... + x^12 + x^15)/Product_{i=1..10} (1 - x^i). (Formerly M1049)

1, 1, 2, 4, 7, 11, 18, 27, 41, 60, 87, 122, 172, 235, 320, 430, 572, 751, 982, 1268, 1629, 2074, 2625, 3297, 4123, 5118, 6324, 7771, 9506, 11567, 14023, 16917, 20335, 24343, 29039, 34510, 40885, 48265, 56811, 66661, 78001, 91001, 105901, 122902, 142291, 164329, 189347

Offset

0,3

Comments

Enumerates certain triangular arrays of integers.

References

J. C. P. Miller, On the enumeration of partially ordered sets of integers, pp. 109-124 of T. P. McDonough and V. C. Mavron, editors, Combinatorics: Proceedings of the Fourth British Combinatorial Conference 1973. London Mathematical Society, Lecture Note Series, Number 13, Cambridge University Press, NY, 1974. The g.f. is in Eq. (10.5).

N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).

Links

Ray Chandler, Table of n, a(n) for n = 0..1000

Index entries for linear recurrences with constant coefficients, signature (1, 1, 1, 0, -2, -2, -3, 0, 2, 5, 4, 4, -2, -5, -6, -7, -2, 1, 7, 8, 7, 1, -2, -7, -6, -5, -2, 4, 4, 5, 2, 0, -3, -2, -2, 0, 1, 1, 1, -1).

Maple

(1+x^3+x^4+x^5+x^6+x^7+x^8+x^9+x^10+x^11+x^12+x^15)/mul(1-x^i, i=1..10);

Mathematica

CoefficientList[Series[(1+Total[x^Range[3, 12] ]+x^15)/Product[1 - x^i, {i, 10}], {x, 0, 50}], x] (* Harvey P. Dale, Jun 24 2018 *)

Crossrefs

Cf. A003402, A003404, A003405, A029073, A256975, A256976, A256977.

Sequence in context: A360891 A073738 A137631 * A261666 A034412 A289131

Adjacent sequences: A003400 A003401 A003402 * A003404 A003405 A003406

Keyword

nonn

Author

N. J. A. Sloane

Extensions

Entry revised by N. J. A. Sloane, Apr 22 2015

Status

approved