A243762 4*n^3 + 5.

1, 5, 9, 37, 113, 261, 505, 869, 1377, 2053, 2921, 4005, 5329, 6917, 8793, 10981, 13505, 16389, 19657, 23333, 27441, 32005, 37049, 42597, 48673, 55301, 62505, 70309, 78737, 87813, 97561, 108005, 119169, 131077, 143753, 157221, 171505, 186629, 202617, 219493

Offset

-1,2

Comments

Squares in the sequence: 1, 9, 5329, for n = -1, 1, 11 respectively. No other square for n < 9*10^9.

Links

Vincenzo Librandi, Table of n, a(n) for n = -1..1000

Index entries for linear recurrences with constant coefficients, signature (4,-6,4,-1).

Formula

G.f.: (-1 + 9*x - 17*x^2 + 35*x^3 - 2*x^4)/(1 - x)^4.

a(n) = 4*A000578(n-1)+5 = 4*A001093(n)+1.

a(n) = 4*a(n-1)-6*a(n-2)+4*a(n-3)-a(n-4) for n>3.

a(n) = A033430(n-1) + 5. - Wesley Ivan Hurt, Jun 10 2014

Maple

A243762:=n->4*n^3 + 5; seq(A243762(n), n=-1..40); # Wesley Ivan Hurt, Jun 10 2014

Mathematica

Table[4 n^3 + 5, {n, -1, 50}] (* or *) CoefficientList[Series[(-1 + 9 x - 17 x^2 + 35 x^3 - 2 x^4)/(1 - x)^4, {x, 0, 40}], x]

Prog

(Magma) [4*n^3+5: n in [-1..40]]; /* or */ I:=[1, 5, 9, 37]; [n le 4 select I[n] else 4*Self(n-1)-6*Self(n-2)+4*Self(n-3)-Self(n-4): n in [1..40]]

Crossrefs

Cf. A000578, A033430.

Sequence in context: A070969 A200376 A098477 * A303801 A304849 A270622

Adjacent sequences: A243759 A243760 A243761 * A243763 A243764 A243765

Keyword

nonn,easy

Author

Vincenzo Librandi, Jun 10 2014

Status

approved