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A336109 First column of dispersion array A120861. 2
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 (list; graph; refs; listen; history; text; internal format)
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 A068398 A293168

Adjacent sequences:  A336106 A336107 A336108 * A336110 A336111 A336112

KEYWORD

nonn

AUTHOR

Petros Hadjicostas, Jul 08 2020

STATUS

approved

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Last modified January 25 19:00 EST 2022. Contains 350572 sequences. (Running on oeis4.)