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A178643
Square array read by antidiagonals. Convolution of a(n) = 2*a(n-1) - a(n-2) and 10^n.
1
1, 10, 2, 100, 19, 4, 1000, 190, 36, 8, 10000, 1900, 361, 68, 16, 100000, 19000, 3610, 686, 128, 32, 1000000, 190000, 36100, 6859, 1304, 240, 64, 10000000, 1900000, 361000, 68590, 13032, 2480, 448, 128, 100000000, 19000000, 3610000, 685900, 130321, 24760, 4720, 832, 256
OFFSET
1,2
COMMENTS
Diagonals sum up to A014824.
Alternating diagonal sum gives decimal expansion of fraction 1/119 (A021123).
LINKS
FORMULA
T(n,k) = 2*T(n,k-1) - T(n-1,k-1) for all n, k > 0, where T(n,0) = 10^n and T(0,k) = 2^k. - Robin Visser, Aug 09 2023
EXAMPLE
Array starts:
1, 2, 4, 8,
10, 19, 36, 68,
100, 190, 361, 686,
1000, 1900, 3610, 6859,
PROG
(Sage)
def a(n, k):
T = [[0 for j in range(k+1)] for i in range(n+1)]
for i in range(n+1): T[i][0] = 10^i
for j in range(1, k+1):
T[0][j] = 2^j
for i in range(1, n+1): T[i][j] = 2*T[i][j-1] - T[i-1][j-1]
return T[n][k] # Robin Visser, Aug 09 2023
CROSSREFS
KEYWORD
easy,nonn,tabl
AUTHOR
Mark Dols, May 31 2010
EXTENSIONS
More terms from Robin Visser, Aug 09 2023
STATUS
approved