A207260 Triangle T(n,k) with T(n,k) = k^2 + (1-(-1)^(n-k))/2.

0, 1, 1, 0, 2, 4, 1, 1, 5, 9, 0, 2, 4, 10, 16, 1, 1, 5, 9, 17, 25, 0, 2, 4, 10, 16, 26, 36, 1, 1, 5, 9, 17, 25, 37, 49, 0, 2, 4, 10, 16, 26, 36, 50, 64, 1, 1, 5, 9, 17, 25, 37, 49, 65, 81, 0, 2, 4, 10, 16, 26, 36

Offset

0,5

Comments

Row sums are A171218(n).

Links

Table of n, a(n) for n=0..61.

Formula

T(n+k, n) = A002522(n) if k is odd.

T(n+k, n) = n^2 = A000290(n) if k is even.

T(2*n, n) = A137928(n), n>0.

T(2*n+1, n+1) = A080335(n).

T(n,0) = A000035(n).

T(n+1,1) = A000034(n).

T(n+2,2) = A010710(n).

T(n+3,3) = A010735(n).

Sum_{k, 0<=k<=n} T(n,k)*x^k = (-1)^n*A007590(n), A000035(n), A171218(n)

for x = -1, 0, 1 respectively.

Example

Triangle begins :
0
1, 1
0, 2, 4
1, 1, 5, 9
0, 2, 4, 10, 16
1, 1, 5, 9, 17, 25
0, 2, 4, 10, 16, 26, 36
1, 1, 5, 9, 17, 25, 37, 49
0, 2, 4, 10, 16, 26, 36, 50, 64
1, 1, 5, 9, 17, 25, 37, 49, 65, 81

Crossrefs

Cf. A000290, A002522, A171218, A137928, A080335

Sequence in context: A065626 A201758 A096110 * A187913 A329458 A332010

Adjacent sequences: A207257 A207258 A207259 * A207261 A207262 A207263

Keyword

easy,nonn,tabl

Author

Philippe Deléham, Feb 16 2012

Status

approved