A255361 - OEIS

A255361

Number of ways n can be represented as x*y+x+y where x>=y>1.

0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 1, 0, 0, 1, 1, 0, 1, 0, 1, 1, 0, 0, 2, 1, 0, 1, 1, 0, 2, 0, 1, 1, 0, 1, 3, 0, 0, 1, 2, 0, 2, 0, 1, 2, 0, 0, 3, 1, 1, 1, 1, 0, 2, 1, 2, 1, 0, 0, 4, 0, 0, 2, 2, 1, 2, 0, 1, 1, 2, 0, 4, 0, 0, 2, 1, 1, 2, 0, 3, 2, 0, 0, 4, 1, 0, 1, 2, 0, 4, 1, 1, 1, 0, 1, 4, 0, 1, 2, 3, 0, 2, 0, 2, 3, 0

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OFFSET

0,24

LINKS

Antti Karttunen, Table of n, a(n) for n = 0..3300

FORMULA

Let d = A000005; then a(n) = floor((d(n+1) - 1)/2) for even n and a(n) = floor((d(n+1) - 3) / 2) for odd n>1. - Ivan Neretin, Sep 07 2015

EXAMPLE

8 = 2*2 + 2 + 2, this is the only representation, so a(8)=1.

23 = 2*7 + 2 + 7 = 3*5 + 3 + 5, two representations, so a(23)=2.

MATHEMATICA

a[n_] := (r = Reduce[x >= y > 1 && n == x*y + x + y, {x, y}, Integers]; Which[r[[0]] === And, 1, r[[0]] === Or, Length[r], True, 0]);

Table[a[n], {n, 0, 105}] (* Jean-François Alcover, Jan 23 2018 *)

PROG

(Python)

TOP = 1000

a = [0]*TOP

for y in range(2, TOP//2):

for x in range(y, TOP//2):

k = x*y + x + y

if k>=TOP: break

a[k]+=1

print(a)

(PARI) a(n) = {nb = 0; for (y=2, n\2, for (x=y, n\2, nb += ((x*y+x+y) == n); ); ); nb; } \\ Michel Marcus, Feb 22 2015

CROSSREFS

Cf. A253975, A254636.

Sequence in context: A295343 A025915 A081285 * A341685 A069844 A233006

Adjacent sequences: A255358 A255359 A255360 * A255362 A255363 A255364

KEYWORD

nonn

AUTHOR

Alex Ratushnyak, Feb 21 2015

EXTENSIONS

More terms from Antti Karttunen, Sep 22 2017

STATUS

approved