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A081275 Shallow diagonal of triangular spiral in A051682. 2
1, 31, 97, 199, 337, 511, 721, 967, 1249, 1567, 1921, 2311, 2737, 3199, 3697, 4231, 4801, 5407, 6049, 6727, 7441, 8191, 8977, 9799, 10657, 11551, 12481, 13447, 14449, 15487, 16561, 17671, 18817, 19999, 21217, 22471, 23761, 25087, 26449, 27847 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,2

COMMENTS

Reflection of A060544 in the horizontal A051682.

Binomial transform of (1, 30, 36, 0, 0, 0, .....).

LINKS

Vincenzo Librandi, Table of n, a(n) for n = 0..1000

Index entries for linear recurrences with constant coefficients, signature (3,-3,1)

FORMULA

a(n) = C(n, 0) + 30*C(n, 1) + 36*C(n, 2).

a(n) = 18*n^2+12*n+1.

G.f.: (1+28*x+7*x^2)/(1-x)^3.

a(0)=1, a(1)=31, a(2)=97, a(n)=3*a(n-1)-3*a(n-2)+a(n-3). - Harvey P. Dale, Jun 30 2011

MATHEMATICA

Table[30Binomial[n, 1]+36Binomial[n, 2]+1, {n, 0, 40}] (* or *) LinearRecurrence[{3, -3, 1}, {1, 31, 97}, 40] (* Harvey P. Dale, Jun 30 2011 *)

CoefficientList[Series[(1 + 28 x + 7 x^2) / (1 - x)^3, {x, 0, 40}], x] (* Vincenzo Librandi, Aug 07 2013 *)

PROG

(PARI) a(n)=18*n^2+12*n+1 \\ Charles R Greathouse IV, Jun 17 2017

CROSSREFS

Cf. A092296.

Sequence in context: A159014 A256323 A142067 * A139509 A187517 A039463

Adjacent sequences:  A081272 A081273 A081274 * A081276 A081277 A081278

KEYWORD

nonn,easy

AUTHOR

Paul Barry, Mar 15 2003

STATUS

approved

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Last modified May 28 07:30 EDT 2022. Contains 354112 sequences. (Running on oeis4.)