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A274979 Integers of the form m*(m + 7)/8. 30
0, 1, 15, 18, 46, 51, 93, 100, 156, 165, 235, 246, 330, 343, 441, 456, 568, 585, 711, 730, 870, 891, 1045, 1068, 1236, 1261, 1443, 1470, 1666, 1695, 1905, 1936, 2160, 2193, 2431, 2466, 2718, 2755, 3021, 3060, 3340, 3381, 3675, 3718, 4026, 4071, 4393, 4440, 4776, 4825 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,3

COMMENTS

Nonnegative values of m are listed in A047393.

Also, numbers h such that 32*h + 49 is a square.

Equivalently, numbers of the form i*(8*i + 7) with i = 0, -1, 1, -2, 2, -3, 3, ...

Infinitely many squares belong to this sequence.

The first bisection is A139278, and 0 followed by the second bisection gives A051870.

Generalized 18-gonal (or octadecagonal) numbers (see the third comment). - Omar E. Pol, Jun 06 2018

Partial sums of A317314. - Omar E. Pol, Jul 28 2018

LINKS

Bruno Berselli, Table of n, a(n) for n = 1..1000

Index entries for linear recurrences with constant coefficients, signature (1,2,-2,-1,1).

FORMULA

O.g.f.: x^2*(1 + 14*x + x^2)/((1 + x)^2*(1 - x)^3).

E.g.f.: (3*(2*x + 1)*exp(-x) + (8*x^2 - 3)*exp(x))/4.

a(n) = (8*(n-1)*n - 3*(2*n-1)*(-1)^n - 3)/4.

EXAMPLE

100 is in the sequence because 100 = 25*(25+7)/8 or also 100 = 4*(8*4-7).

MATHEMATICA

Select[m = Range[0, 200]; m (m + 7)/8, IntegerQ] (* Jean-Fran├žois Alcover, Jul 21 2016 *)

Select[Table[(m(m+7))/8, {m, 0, 200}], IntegerQ] (* or *) LinearRecurrence[ {1, 2, -2, -1, 1}, {0, 1, 15, 18, 46}, 50] (* Harvey P. Dale, May 07 2019 *)

PROG

(Sage)

def A274979_list(len):

    h = lambda m: m*(m+7)/8

    return [h(m) for m in (0..len) if h(m) in ZZ]

print A274979_list(199) # Peter Luschny, Jul 18 2016

(MAGMA) [t: m in [0..200] | IsIntegral(t) where t is m*(m+7)/8];

CROSSREFS

Cf. sequences of the form m*(m+k)/(k+1) listed in A274978.

Cf. similar sequences listed in A299645.

Cf. A317314.

Sequences of generalized k-gonal numbers: A001318 (k=5), A000217 (k=6), A085787 (k=7), A001082 (k=8), A118277 (k=9), A074377 (k=10), A195160 (k=11), A195162 (k=12), A195313 (k=13), A195818 (k=14), A277082 (k=15), A274978 (k=16), A303305 (k=17), this sequence (k=18), A303813 (k=19), A218864 (k=20), A303298 (k=21), A303299 (k=22), A303303 (k=23), A303814 (k=24), A303304 (k=25), A316724 (k=26), A316725 (k=27), A303812 (k=28), A303815 (k=29), A316729 (k=30).

Sequence in context: A125006 A125008 A290015 * A083823 A222682 A220787

Adjacent sequences:  A274976 A274977 A274978 * A274980 A274981 A274982

KEYWORD

nonn,easy

AUTHOR

Bruno Berselli, Jul 15 2016

STATUS

approved

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Last modified February 22 13:51 EST 2020. Contains 332136 sequences. (Running on oeis4.)