A336109 First column of dispersion array A120861.

1, 2, 3, 4, 5, 6, 8, 9, 10, 11, 13, 14, 15, 16, 17, 18, 20, 21, 22, 23, 25, 26, 27, 28, 29, 30, 32, 33, 34, 35, 37, 38, 39, 40, 42, 43, 44, 45, 46, 47, 49, 50, 51, 52, 54, 55, 56, 57, 58, 59, 61, 62, 63, 64, 66, 67, 68, 69, 71, 72, 73, 74, 75, 76, 78, 79, 80, 81, 83, 84, 85, 86, 87, 88, 90, 91, 92, 93, 95, 96

Offset

1,2

Comments

For n = 1 to 34, we have a(n) = A039216(n), but a(35) = 42 <> = 41 = A039216(35).

Is this the same as A188040? - R. J. Mathar, Jul 22 2020

Indeed, it seems that A336109(1) = A188040(1) and A336109(n) = A188040(n-1) for n >= 3, but A336109(2) = 2 does not appear in A188040. Because of the way A120861 is constructed (cf. Michel Marcus's PARI program below), a(2) = 2 cannot be omitted. - Petros Hadjicostas, Jul 22 2020

Links

Table of n, a(n) for n=1..80.

Clark Kimberling, The equation (j+k+1)^2 - 4*k = Q*n^2 and related dispersions, Journal of Integer Sequences, 10 (2007), Article #07.2.7; see Section 5.

Prog

(PARI) /* This is Michel Marcus's program from A120861. */
f(n) = 3*n + 2*sqrtint(2*n^2) + 2;
unused(listus) = {my(v=vecsort(Vec(listus))); for (i=1, vecmax(v), if (!vecsearch(v, i), return (i)); ); };
D(nb) = {my(m = matrix(nb, nb), t); my(listus = List); for (g=1, nb, if (g==1, t = 1, t = unused(listus)); m[g, 1]=t; listput(listus, t); t = f(t); m[g, 2]=t; listput(listus, t); for (h=3, nb, t = 6*m[g, h-1] - m[g, h-2]; m[g, h] = t; listput(listus, t); ); ); m; };
firstcol(nb) = my(m=D(nb)); vector(nb, k, m[k, 1]);

Crossrefs

Cf. A039216, A120861, A188040.

Sequence in context: A055492 A005459 A039216 * A091208 A353202 A068398

Adjacent sequences: A336106 A336107 A336108 * A336110 A336111 A336112

Keyword

nonn

Author

Petros Hadjicostas, Jul 08 2020

Status

approved