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A119865 Triangle T(n,k), 0<=k<=n, read by rows, given by [1, 1, 0, 1, 0, 0, 0, 0, 0, ...] DELTA [1, 0, 1, 0, 1, 0, 0, 0, 0, 0, ...] where DELTA is the operator defined in A084938. 0
1, 1, 1, 2, 3, 1, 4, 9, 6, 1, 8, 25, 26, 10, 1, 16, 65, 95, 60, 15, 1, 32, 161, 308, 279, 120, 21, 1, 64, 385, 917, 1099, 693, 217, 28, 1, 128, 897, 2566, 3856, 3256, 1526, 364, 36, 1 (list; table; graph; refs; listen; history; text; internal format)
OFFSET

0,4

LINKS

Table of n, a(n) for n=0..44.

FORMULA

Sum_{k =0..n}T(n,k)= A087944(n).

Sum_{k=0..n}(-1)^k*2^(n-k)*T(n,k)= n^2-n+1= A002061(n).

Sum_{k=0..n}(-1)^k*T(n,k)=0^n= A000007(n).

G.f.: (1-2*x-2*x*y++x^2+x^2*y+x^2*y^2)/(1-3*x-3*x*y+2*x^2+4*x^2*y+3*x^2*y^2-x^3*y^2-x^3*y^3). - Philippe Deléham, Nov 09 2013

T(n,k) = 3*T(n-1,k) + 3*T(n-1,k-1) - 2*T(n-2,k) - 4*T(n-2,k-1) - 3*T(n-2,k-2) + T(n-3,k-2) + T(n-3,k-3), T(0,0) = T(1,0) = T(1,1) = T(2,2) = 1, T(2,0) = 2, T(2,1) = 3, T(n,k) = 0 if k<0 or if k>n. - Philippe Deléham, Nov 09 2013

EXAMPLE

Triangle begins:

1;

1, 1;

2, 3, 1;

4, 9, 6, 1;

8, 25, 26, 10, 1;

16, 65, 95, 60, 15, 1;

32, 161, 308, 279, 120, 21, 1;

64, 385, 917, 1099, 693, 217, 28, 1;

128, 897, 2566, 3856, 3256, 1526, 364, 36, 1;

CROSSREFS

Cf. Diagonals : A011782, A002064 ; A000012, A000217.

Sequence in context: A121340 A231206 A165241 * A177896 A193920 A076732

Adjacent sequences:  A119862 A119863 A119864 * A119866 A119867 A119868

KEYWORD

easy,nonn,tabl

AUTHOR

Philippe Deléham, Jul 31 2006

STATUS

approved

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Last modified November 13 01:32 EST 2018. Contains 317118 sequences. (Running on oeis4.)