A048473 -id:A048473 - cp's OEIS frontend

A067763 Square array read by antidiagonals of base n numbers written as 122...222 with k 2's (and a suitable interpretation for n=0, 1 or 2).

1, 2, 1, 2, 3, 1, 2, 5, 4, 1, 2, 7, 10, 5, 1, 2, 9, 22, 17, 6, 1, 2, 11, 46, 53, 26, 7, 1, 2, 13, 94, 161, 106, 37, 8, 1, 2, 15, 190, 485, 426, 187, 50, 9, 1, 2, 17, 382, 1457, 1706, 937, 302, 65, 10, 1, 2, 19, 766, 4373, 6826, 4687, 1814, 457, 82, 11, 1, 2, 21, 1534, 13121

Offset: 0

Henry Bottomley, Feb 06 2002

Start with a node; step one is to connect that node to n+1 new nodes so that it is of degree n+1; further steps are to connect each existing node of degree 1 to n new nodes so that it is of degree n+1; T(n,k) is the total number of nodes after k steps.

			Rows start: 1,2,2,2,2,2,...; 1,3,5,7,9,11,...; 1,4,10,22,46,94,...; 1,5,17,53,161,485,... T(3,2) =122 base 3 =17.

Rows include A040000, A005408, A033484, A048473, A020989, A057651, A061801 etc. For negative n (not shown) absolute values of rows would effectively include A000012, A014113, A046717.

T(n, k) =((n+1)*n^k-2)/(n-1) [with T(1, k)=2k+1] =n*T(n, k-1)+2 =(n+1)*T(n, k-1)-n*T(n, k-2) =T(n, k-1)+(1+1/n)*n^k =A055129(k, n)+A055129(k-1, n). Coefficient of x^k in expansion of (1+x)/((1-x)(1-nx)).

A155158 Period 4: repeat [1, 5, 7, 3].

Original entry on oeis.org

1, 5, 7, 3, 1, 5, 7, 3, 1, 5, 7, 3, 1, 5, 7, 3, 1, 5, 7, 3, 1, 5, 7, 3, 1, 5, 7, 3, 1, 5, 7, 3, 1, 5, 7, 3, 1, 5, 7, 3, 1, 5, 7, 3, 1, 5, 7, 3, 1, 5, 7, 3, 1, 5, 7, 3, 1, 5, 7, 3, 1, 5, 7, 3, 1, 5, 7, 3, 1, 5, 7, 3, 1, 5, 7, 3, 1, 5, 7, 3, 1, 5, 7, 3, 1, 5

Offset: 0

Paul Curtz, Jan 21 2009

Index entries for linear recurrences with constant coefficients, signature (1,-1,1).

Cf. A010694, A010696, A048473, A105398.

&cat [[1, 5, 7, 3]^^30]; // Wesley Ivan Hurt, Jul 08 2016

seq(op([1, 5, 7, 3]), n=0..50); # Wesley Ivan Hurt, Jul 08 2016

PadRight[{}, 300, {1, 5, 7, 3}] (* Wesley Ivan Hurt, Jul 08 2016 *)

a(n) = A048473(n) mod 10.
First differences: a(n+1)-a(n) = (-1)^floor(n/2)*A010694(n+1).
Second differences: a(n+2)-2*a(n+1)+a(n) = (-1)^floor(1+n/2)*A010696(n).
Third differences: a(n+3)-3*a(n+2)+3*a(n+1)-a(n) = (-1)^floor((n+3)/2)*A105398(n).
G.f.: (1+4*x+3*x^2)/(1-x+x^2-x^3). - Colin Barker, Feb 28 2012
a(n) = a(n-1) - a(n-2) + a(n-3) for n>2. - Wesley Ivan Hurt, Jul 08 2016

A238207 Square array T(n,k), n>=0, k>=0, read by antidiagonals, where T(0,k) is A032766(k) and T(n,k) = 3*T(n-1,k) + 2 for n>0.

Original entry on oeis.org

0, 1, 2, 3, 5, 8, 4, 11, 17, 26, 6, 14, 35, 53, 80, 7, 20, 44, 107, 161, 242, 9, 23, 62, 134, 323, 485, 728, 10, 29, 71, 188, 404, 971, 1457, 2186, 12, 32, 89, 215, 566, 1214, 2915, 4373, 6560, 13, 28, 98, 269, 647, 1700, 3644, 8747, 13121, 19682, 15, 41, 116

Offset: 0

Philippe Deléham, Feb 20 2014

Permutation of nonnegative integers.

			Square array begins:
0, 1, 3, 4, 6, 7, 9, 10, ...
2, 5, 11, 14, 20, 23, 29, 32, ...
8, 17, 35, 44, 62, 71, 89, 98, ...
26, 53, 107, 134, 188, 215, 269, 296, ...
80, 161, 323, 404, 566, 647, 809, 890, ...
242, 485, 971, 1214, 1700, 1943, 2429, 2672, ...
728, 1457, 2915, 3644, 5102, 5831, 7289, 8018, ...
2186, 4373, 8747, 10934, 15308, 17495, 21869, 24056, ...
...

Cf. A024023, A027107, A032766, A048473, A171498, A198643, A198644, A198645, A198646.

T(n,k) = T(0,k)*3^n + T(n,0) where T(0,k) = A032766(k) and T(n,0) = 3^n - 1 = A024023(n).

cp's OEIS Frontend

A067763 Square array read by antidiagonals of base n numbers written as 122...222 with k 2's (and a suitable interpretation for n=0, 1 or 2).

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A155158 Period 4: repeat [1, 5, 7, 3].

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A238207 Square array T(n,k), n>=0, k>=0, read by antidiagonals, where T(0,k) is A032766(k) and T(n,k) = 3*T(n-1,k) + 2 for n>0.

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