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A023545 Convolution of natural numbers >= 2 and natural numbers >= 3. 1
6, 17, 34, 58, 90, 131, 182, 244, 318, 405, 506, 622, 754, 903, 1070, 1256, 1462, 1689, 1938, 2210, 2506, 2827, 3174, 3548, 3950, 4381, 4842, 5334, 5858, 6415, 7006, 7632, 8294, 8993, 9730, 10506, 11322, 12179, 13078, 14020, 15006, 16037 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,1

LINKS

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

László Németh, Tetrahedron trinomial coefficient transform, arXiv:1905.13475 [math.CO], 2019.

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

FORMULA

a(n) = n*(n^2 + 12*n + 23)/6. - Ralf Stephan, Feb 15 2004; corrected by Lucas Sidiropoulos (lsid77(AT)yahoo.com), Jun 23 2008

a(n) = 4*a(n-1)-6*a(n-2)+4*a(n-3)-a(n-4). G.f.: x*(2-x)*(3-2*x)/(1-x)^4. - Colin Barker, Jun 20 2012

MATHEMATICA

CoefficientList[Series[(2-x)*(3-2*x)/(1-x)^4, {x, 0, 40}], x] (* Vincenzo Librandi, Jun 29 2012 *)

LinearRecurrence[{4, -6, 4, -1}, {6, 17, 34, 58}, 50] (* Harvey P. Dale, Aug 10 2014 *)

PROG

(MAGMA) I:=[6, 17, 34, 58]; [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..50]]; // Vincenzo Librandi, Jun 29 2012

CROSSREFS

Sequence in context: A066486 A301719 A056109 * A038633 A083045 A012277

Adjacent sequences:  A023542 A023543 A023544 * A023546 A023547 A023548

KEYWORD

nonn,easy

AUTHOR

Clark Kimberling

STATUS

approved

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Last modified December 5 08:34 EST 2021. Contains 349543 sequences. (Running on oeis4.)