A255168 - OEIS

A255168

Rectangular array A read by upward antidiagonals in which row n is the set of positive integers that are congruent to {(1 + 2^n*(3 + 2*(-1)^n))/3, 2^(n + 1), (1 + 2^n*(15 + 2*(-1)^n))/3} (mod 2^(n+2)).

1, 7, 4, 3, 8, 5, 27, 16, 15, 9, 11, 32, 19, 23, 12, 107, 64, 59, 35, 24, 13, 43, 128, 75, 91, 48, 31, 17, 427, 256, 235, 139, 96, 51, 39, 20, 171, 512, 299, 363, 192, 123, 67, 40, 21, 1707, 1024, 939, 555, 384, 203, 155, 80, 47, 25

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OFFSET

1,2

LINKS

Table of n, a(n) for n=1..55.

FORMULA

A(n,k) = A(n,k-3) + 2^(n+2), n >= 1, k > 3, with initial conditions A(n,1) = (1 + 2^n*(3 + 2*(-1)^n))/3, A(n,2) = 2^(n+1), A(n,3) = A(n,1) + 2^(n+1).

A(n,k) == (1 + 2^n*(3 + 2*(-1)^n))/3 (mod 2^(n+1) or 2^(n+1) (mod 2^(n+2)).

EXAMPLE

Array A begins:

. 1 4 5 9 12 13 17 20 21 25

. 7 8 15 23 24 31 39 40 47 55

. 3 16 19 35 48 51 67 80 83 99

. 27 32 59 91 96 123 155 160 187 219

. 11 64 75 139 192 203 267 320 331 395

. 107 128 235 363 384 491 619 640 747 875

. 43 256 299 555 768 811 1067 1280 1323 1579

. 427 512 939 1451 1536 1963 2475 2560 2987 3499

. 171 1024 1195 2219 3072 3243 4267 5120 5291 6315

. 1707 2048 3755 5803 6144 7851 9899 10240 11947 13995

MATHEMATICA

(* Array antidiagonals flattened: *)

a[n_, 1] := (1 + 2^n*(3 + 2*(-1)^n))/3; a[n_, 2] := 2^(n + 1); a[n_, 3] := a[n, 1] + 2^(n + 1); a[n_, k_] := a[n, k - 3] + 2^(n + 2); Flatten[Table[a[n - k + 1, k], {n, 10}, {k, n}]]

CROSSREFS

A047610 (row 1).

Sequence in context: A293237 A316250 A199727 * A257776 A364488 A065477

Adjacent sequences: A255165 A255166 A255167 * A255169 A255170 A255171

KEYWORD

nonn,tabl

AUTHOR

L. Edson Jeffery, May 04 2015

STATUS

approved