A048506 a(n) = T(0,n), array T given by A048505.

1, 2, 7, 25, 81, 241, 673, 1793, 4609, 11521, 28161, 67585, 159745, 372737, 860161, 1966081, 4456449, 10027009, 22413313, 49807361, 110100481, 242221057, 530579457, 1157627905, 2516582401, 5452595201, 11777605633, 25367150593, 54492397569, 116769423361

Offset: 0

Author

Clark Kimberling

Keywords

• nonn
• easy

Comments

n-th difference of a(n), a(n-1), ..., a(0) is (1, 4, 9, 16, 25, ...).

Similar to A000697 in so far as it can be seen as the transform of 1, 1, 4, 9, 16, ... by a variant of the boustrophedon algorithm (see the Sage implementation). - Peter Luschny, Oct 30 2014

Links

• Vincenzo Librandi, Table of n, a(n) for n = 0..2000
• Index entries for linear recurrences with constant coefficients, signature (7,-18,20,-8).

Crossrefs

Cf. A048505, A000697.

Programs

Magma

[n*(n+1)*2^(n-2) + 1: n in [0..30]]; // Vincenzo Librandi, Sep 26 2011

Mathematica

LinearRecurrence[{7,-18,20,-8}, {1,2,7,25}, 30] (* Jean-François Alcover, Jun 11 2019 *)

PARI

Vec(-(8*x^3-11*x^2+5*x-1)/((x-1)*(2*x-1)^3) + O(x^100)) \\ Colin Barker, Nov 26 2014

Sage

def sq():
    yield 1
    for n in PositiveIntegers():
        yield n*n
def bous_variant(f):
    k = 0
    am = next(f)
    a = [am]
    while True:
        yield am
        am = next(f)
        a.append(am)
        for j in range(k,-1,-1):
            am += a[j]
            a[j] = am
        k += 1
b = bous_variant(sq())
print([next(b) for  in range(26)]) # _Peter Luschny, Oct 30 2014

Formula

a(n) = n*(n+1)*2^(n-2) + 1 = A001788(n) + 1. - Ralf Stephan, Jan 16 2004

a(n) = 7*a(n-1)-18*a(n-2)+20*a(n-3)-8*a(n-4). - Colin Barker, Nov 26 2014

G.f.: -(8*x^3-11*x^2+5*x-1) / ((x-1)*(2*x-1)^3). - Colin Barker, Nov 26 2014