The On-Line Encyclopedia of Integer Sequences (OEIS)

Revision History for A100135

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A100135

a(n) = Sum_{k=0..floor(n/6)} C(n-3k,3k) * 2^k.
(history; published version)

#24 by Michel Marcus at Sun Dec 24 02:30:02 EST 2023

STATUS

reviewed

approved

#23 by Joerg Arndt at Sun Dec 24 01:23:23 EST 2023

STATUS

proposed

reviewed

#22 by Joerg Arndt at Sun Dec 24 01:23:20 EST 2023

STATUS

editing

proposed

#21 by Joerg Arndt at Sun Dec 24 01:23:17 EST 2023

FORMULA

G.f.: (1-x)^2/((1-x)^3 - 2x2*x^6).

STATUS

proposed

editing

#20 by Stefano Spezia at Sat Dec 23 15:19:54 EST 2023

STATUS

editing

proposed

#19 by Stefano Spezia at Sat Dec 23 15:19:48 EST 2023

DATA

1, 1, 1, 1, 1, 1, 3, 9, 21, 41, 71, 113, 173, 269, 443, 777, 1413, 2577, 4615, 8065, 13813, 23413, 39691, 67801, 116973, 203337, 354519, 617345, 1071197, 1851677, 3192731, 5501033, 9485621, 16381185, 28330119, 49035777, 84883621, 146875717, 253983307, 438968761

KEYWORD

easy,nonn,easy,changed

STATUS

proposed

editing

#18 by Stefano Spezia at Sat Dec 23 02:07:02 EST 2023

STATUS

editing

proposed

#17 by Stefano Spezia at Sat Dec 23 02:06:41 EST 2023

MATHEMATICA

LinearRecurrence[{3, -3, 1, 0, 0, 2}, {1, 1, 1, 1, 1, 1}, 38] (* or *) a[0]=1; a[1]=1; a[2]=1; a[3]=1; a[4]=1; a[5]=1; a[n_]:= a[n]=3*a[n-1]-3*a[n-2]+a[n-3]+2*a[n-6]; Table[a[n], {n, 0, 37}](* James C. McMahon, Dec 22 2023 *)

LinearRecurrence[{3, -3, 1, 0, 0, 2}, {1, 1, 1, 1, 1, 1}, 38] (* James C. McMahon, Dec 22 2023 *)

STATUS

proposed

editing

Discussion

Sat Dec 23

02:07

Stefano Spezia: Removed

#16 by James C. McMahon at Fri Dec 22 17:52:15 EST 2023

STATUS

editing

proposed

Discussion

Sat Dec 23

02:05

Stefano Spezia: For linear recurrence Mathematica code is preferred the first version you submitted…

#15 by James C. McMahon at Fri Dec 22 17:50:51 EST 2023

MATHEMATICA

LinearRecurrence[{3, -3, 1, 0, 0, 2}, {1, 1, 1, 1, 1, 1}, 38] (* _or *) a[0]=1; a[1]=1; a[2]=1; a[3]=1; a[4]=1; a[5]=1; a[n_]:= a[n]=3*a[n-1]-3*a[n-2]+a[n-3]+2*a[n-6]; Table[a[n], {n, 0, 37}](* _James C. McMahon_, Dec 22 2023 *)

STATUS

proposed

editing