A147721 a(n) = C(2,n) DELTA C(0,n).

1, 1, 1, 3, 4, 1, 11, 17, 7, 1, 41, 72, 40, 10, 1, 153, 301, 208, 72, 13, 1, 571, 1244, 1021, 446, 113, 16, 1, 2131, 5093, 4819, 2525, 813, 163, 19, 1, 7953, 20688, 22104, 13452, 5218, 1336, 222, 22, 1, 29681, 83481, 99192, 68568, 30986, 9586, 2042, 290, 25, 1

Offset

0,4

Comments

Triangle T equal to [1,2,1,0,0,0,...] DELTA [1,0,0,0,...] for Deléham DELTA as in A084938.

T = A147720*A007318. Row sums are A147722.

Links

Indranil Ghosh, Rows 0..100, flattened

Formula

Riordan array ((1-3x)/(1-4x+x^2), x(1-x)/(1-4x+x^2)).

T(n,k) = 4*T(n-1,k) + T(n-1,k-1) - T(n-2,k) - T(n-2,k-1), n > 1. - Philippe Deléham, Feb 13 2012

G.f.: (1-3*x)/(1-4*x+(1+y)*x^2-y*x). - Philippe Deléham, Feb 13 2012

Sum_{k=0..n} T(n,k)*x^k = A000007(n), A001835(n), A147722(n), A084120(n) for x = -1, 0, 1, 2 respectively. - Philippe Deléham, Feb 13 2012

Example

Triangle begins
    1;
    1,   1;
    3,   4,   1;
   11,  17,   7,   1;
   41,  72,  40,  10,   1;
  153, 301, 208,  72,  13,   1;

Mathematica

nmax=9; Flatten[CoefficientList[Series[CoefficientList[Series[(1 - 3*x)/(1 - 4*x + (1 + y)*x^2 - y*x), {x, 0, nmax}], x], {y, 0, nmax}], y]] (* Indranil Ghosh, Mar 10 2017, after Philippe Deléham *)

Crossrefs

Cf. A129267, A007318, A147703.

Sequence in context: A054649 A380113 A138263 * A172094 A114608 A154602

Adjacent sequences: A147718 A147719 A147720 * A147722 A147723 A147724

Keyword

easy,nonn,tabl

Author

Paul Barry, Nov 11 2008

Status

approved