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A188107 Triangle T(n,k) with the coefficient [x^k] of 1/(1 - x - 2*x^2 + x^3)^(n-k+1) in row n, column k. 2
1, 1, 1, 1, 2, 3, 1, 3, 7, 4, 1, 4, 12, 14, 9, 1, 5, 18, 31, 35, 14, 1, 6, 25, 56, 87, 70, 28, 1, 7, 33, 90, 175, 207, 154, 47, 1, 8, 42, 134, 310, 476, 504, 306, 89, 1, 9, 52, 189, 504, 941, 1274, 1137, 633, 155, 1, 10, 63, 256, 770, 1680, 2745, 3188, 2571 (list; table; graph; refs; listen; history; text; internal format)
OFFSET

0,5

COMMENTS

Modified versions of the generating function for the diagonal, A006053, are related to rhombus substitution tilings (see A187065, A187066 and A187067).

LINKS

Nathaniel Johnston, Rows n = 0..100, flattened

FORMULA

Sum_{k=0..n} T(n,k) = A001654(n+1).

T(n,k) = T(n-1,k) + T(n-1,k-1) + 2*T(n-2,k-2) - T(n-3,k-3). - Philippe Deléham, Feb 24 2012

EXAMPLE

The triangle starts in row n=0 as

  1;

  1,   1;

  1,   2,   3;

  1,   3,   7,   4;

  1,   4,  12,  14,   9;

  1,   5,  18,  31,  35,  14;

  1,   6,  25,  56,  87,  70,  28;

  1,   7,  33,  90, 175, 207, 154,  47;

  1,   8,  42, 134, 310, 476, 504, 306,  89;

MAPLE

A188107 := proc(n, k) 1/(1-x-2*x^2+x^3)^(n-k+1) ; coeftayl(%, x=0, k) ; end proc:

seq(seq(A188107(n, k), k=0..n), n=0..10) ; # R. J. Mathar, Mar 22 2011

CROSSREFS

Cf. A001654, A187065, A187066, A187067.

Cf. Columns: A000012, A000027, A055998.

Sequence in context: A292915 A271700 A136555 * A174014 A236376 A063967

Adjacent sequences:  A188104 A188105 A188106 * A188108 A188109 A188110

KEYWORD

nonn,easy,tabl

AUTHOR

L. Edson Jeffery, Mar 20 2011

STATUS

approved

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Last modified August 21 18:38 EDT 2019. Contains 326168 sequences. (Running on oeis4.)