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A099900 XOR difference triangle, read by rows, of A099901 (in leftmost column) such that the main diagonal equals A099901 shift left and divided by 2. 3
1, 2, 3, 6, 4, 7, 14, 8, 12, 11, 22, 24, 16, 28, 23, 46, 56, 32, 48, 44, 59, 118, 88, 96, 64, 112, 92, 103, 206, 184, 224, 128, 192, 176, 236, 139, 278, 472, 352, 384, 256, 448, 368, 412, 279, 558, 824, 736, 896, 512, 768, 704, 944, 556, 827, 1654, 1112, 1888, 1408 (list; table; graph; refs; listen; history; text; internal format)
OFFSET

0,2

COMMENTS

Central terms of rows equal powers of 2: T(n,[n/2]) = 2^n for n>=0. The leftmost column is A099901. The diagonal forms A099902 and equals the XOR BINOMIAL transform of A099901.

LINKS

Table of n, a(n) for n=0..58.

FORMULA

T(n, [n/2]) = 2^n. T(n+1, 0) = 2*T(n, n) (n>=0); T(0, 0)=1; T(n, k) = T(n, k-1) XOR T(n-1, k-1) for n>k>0. T(n, k) = SumXOR_{i=0..k} (C(k, i)mod 2)*T(n-i, 0), where SumXOR is the analog of summation under the binary XOR operation and C(k, i)mod 2 = A047999(k, i).

EXAMPLE

Rows begin:

[_1],

[_2,3],

[6,_4,7],

[14,_8,12,11],

[22,24,_16,28,23],

[46,56,_32,48,44,59],

[118,88,96,_64,112,92,103],

[206,184,224,_128,192,176,236,139],

[278,472,352,384,_256,448,368,412,279],

[558,824,736,896,_512,768,704,944,556,827],

[1654,1112,1888,1408,1536,_1024,1792,1472,1648,1116,1895],...

notice that the column terms equal twice the diagonal (with offset), and that the central terms in the rows form the powers of 2.

PROG

(PARI) T(n, k)=if(n<k || k<0, 0, if(k==0, if(n==0, 1, 2*T(n-1, n-1)), bitxor(T(n, k-1), T(n-1, k-1))); )

CROSSREFS

Cf. A099884, A099901, A099902.

Sequence in context: A092283 A266191 A273338 * A193903 A138728 A291604

Adjacent sequences:  A099897 A099898 A099899 * A099901 A099902 A099903

KEYWORD

eigen,nonn,tabl

AUTHOR

Paul D. Hanna, Oct 29 2004

STATUS

approved

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Last modified February 23 00:28 EST 2020. Contains 332157 sequences. (Running on oeis4.)