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A340266 The number of degrees of freedom in a quadrilateral cell for a serendipity finite element space of order n. 1
4, 8, 12, 17, 23, 30, 38, 47, 57, 68, 80, 93, 107, 122, 138, 155, 173, 192, 212, 233, 255, 278, 302, 327, 353, 380, 408, 437, 467, 498, 530, 563, 597, 632, 668, 705, 743, 782, 822, 863, 905, 948, 992, 1037, 1083, 1130, 1178, 1227, 1277 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,1

LINKS

Table of n, a(n) for n=1..49.

DefElement, Serendipity

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

FORMULA

a(1) = 4, a(n) = n*(n+3)/2 + 3 (if n > 1).

From Stefano Spezia, Jan 02 2021: (Start)

G.f.: x*(4 - 4*x + x^3)/(1 - x)^3.

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

a(n) = (A111802(n+2)+1)/2 + 2. - Hugo Pfoertner, Jan 02 2021

MATHEMATICA

A340266[n_] := Module[{a}, a[1] = 4; a[i_] := a[i] = i*(i + 3)/2 + 3; a[n]]; Table[A340266[n], {n, 1, 49}] (* Robert P. P. McKone, Jan 29 2021 *)

LinearRecurrence[{3, -3, 1}, {4, 8, 12, 17}, 50] (* Harvey P. Dale, Oct 24 2021 *)

PROG

(Python) print([4 if n == 1 else n * (n + 3) // 2 + 3 for n in range(1, 50)])

(PARI) a(n) = if (n==1, 4, n*(n+3)/2 + 3); \\ Michel Marcus, Jan 04 2021

CROSSREFS

Sequence in context: A311552 A311553 A311554 * A194274 A098573 A092753

Adjacent sequences: A340263 A340264 A340265 * A340267 A340268 A340269

KEYWORD

nonn,easy

AUTHOR

Matthew Scroggs, Jan 02 2021

STATUS

approved

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Last modified February 1 07:16 EST 2023. Contains 359981 sequences. (Running on oeis4.)