A371100 Array A read by upward antidiagonals in which the entry A(n,k) in row n and column k is defined by A(n, k) = 4^n*(6*k - 3 - 2*(-1)^n) + (4^n - 1)/3, n,k >= 1.

21, 21, 45, 341, 117, 69, 341, 725, 213, 93, 5461, 1877, 1109, 309, 117, 5461, 11605, 3413, 1493, 405, 141, 87381, 30037, 17749, 4949, 1877, 501, 165, 87381, 185685, 54613, 23893, 6485, 2261, 597, 189, 1398101, 480597, 283989, 79189, 30037, 8021, 2645, 693, 213, 1398101, 2970965, 873813, 382293, 103765, 36181, 9557, 3029, 789, 237

Offset

1,1

Links

Paolo Xausa, Table of n, a(n) for n = 1..11325 (first 150 antidiagonals, flattened).

Formula

A(n, k) = A007283(n)*A257852(n,k) + A079319(n).

A(n, k) = A371094(A257852(n,k)).

A(n+2, k) = 5 + 16*A(n,k).

Example

The top left corner of the array:
n\k|      1       2       3        4        5        6        7        8
---+--------------------------------------------------------------------------
1  |     21,     45,     69,      93,     117,     141,     165,     189, ...
2  |     21,    117,    213,     309,     405,     501,     597,     693, ...
3  |    341,    725,   1109,    1493,    1877,    2261,    2645,    3029, ...
4  |    341,   1877,   3413,    4949,    6485,    8021,    9557,   11093, ...
5  |   5461,  11605,  17749,   23893,   30037,   36181,   42325,   48469, ...
6  |   5461,  30037,  54613,   79189,  103765,  128341,  152917,  177493, ...
7  |  87381, 185685, 283989,  382293,  480597,  578901,  677205,  775509, ...
8  |  87381, 480597, 873813, 1267029, 1660245, 2053461, 2446677, 2839893, ...
...

Mathematica

A371100[n_, k_] := 4^n*(6*k - 3 - 2*(-1)^n) + (4^n - 1)/3;
Table[A371100[n - k + 1, k], {n, 10}, {k, n}] (* Paolo Xausa, Apr 21 2024 *)

Prog

(PARI)
up_to = 55;
A371100sq(n, k) = 4^n*(6*k - 3 - 2*(-1)^n) + (4^n - 1)/3;
A371100list(up_to) = { my(v = vector(up_to), i=0); for(a=1, oo, for(col=1, a, i++; if(i > up_to, return(v)); v[i] = A371100sq((a-(col-1)), col))); (v); };
v371100 = A371100list(up_to);
A371100(n) = v371100[n];

Crossrefs

Cf. A007283, A079319, A257852, A371094, A371101.

Cf. A372351 (same terms, in different order), A372290 (sorted into ascending order, without duplicates), A372293 (odd numbers that do not occur here).

Leftmost column is A144864 duplicated, without its initial 1.

Row 1: A102603.

Sequence in context: A151910 A040421 A022355 * A048245 A246034 A220689

Adjacent sequences: A371097 A371098 A371099 * A371101 A371102 A371103

Keyword

nonn,tabl

Author

Antti Karttunen and Ali Sada, Apr 18 2024

Status

approved