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 A268317 Irregular triangle read by rows: T(n,k) gives the columns sum in the table Fib(n+1) X Fib(n), where k = 1..Fib(n), and 1's are assigned to cells on the longest diagonal path. 3
 0, 1, 2, 2, 2, 2, 3, 2, 2, 3, 2, 3, 2, 2, 3, 2, 3, 3, 2, 3, 2, 2, 3, 2, 3, 3, 2, 3, 2, 3, 3, 2, 3, 2, 2, 3, 2, 3, 3, 2, 3, 2, 3, 3, 2, 3, 3, 2, 3, 2, 3, 3, 2, 3, 2, 2, 3, 2, 3, 3, 2, 3, 2, 3, 3, 2, 3, 3, 2, 3, 2, 3, 3, 2, 3, 2, 3, 3, 2, 3, 3, 2, 3, 2, 3, 3, 2, 3, 2, 2, 3, 2, 3, 3, 2, 3, 2, 3, 3, 2, 3 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,3 COMMENTS Inspired by sun flower spirals which come in Fib(i) and Fib(i+1) numbers in opposite directions. The present case of the Fib(n+1) X Fib(n) table has the following properties: (i) Columns sum create the present irregular triangle. (ii) Rows sum create the irregular triangle A268318. (iii) The row sum of each of these irregular triangles is conjectured to be A000071. (iv) The first differences of the sequence of half of the voids (0's) are conjectured to give A191797. See illustrations in the links. LINKS Table of n, a(n) for n=0..100. Kival Ngaokrajang, Illustration of initial terms, Sun flower spirals EXAMPLE Irregular triangle begins: 1 2 2 2 2 3 2 2 3 2 3 2 2 3 2 3 3 2 3 2 2 3 2 3 3 2 3 2 3 3 2 3 2 ... PROG (Small Basic) TextWindow.Write("0, 1, 2, 2, 2, 2, 3, 2, ") t[4][1] = 2 t[4][2] = 3 t[4][3] = 2 k[3] = 2 k[4] = 3 For n = 5 To 12 k[n] = k[n-1]+k[n-2] c = math.Ceiling(k[n]/2) i1 = 1 For j = 1 To k[n] If Math.Remainder(k[n], 2)<>0 Then If j > c then t[n][j] = t[n][j-2*i1] i1 = i1 + 1 Else t[n][j] = t[n-1][j] EndIf Else If j <= c then t[n][j] = t[n-1][j] Else if j = c+1 Then t[n][j] = t[n][j-1] else t[n][j] = t[n][j-(2*i1+1)] i1 = i 1+ 1 endif EndIf EndIf TextWindow.Write(t[n][j]+", ") EndFor EndFor CROSSREFS Cf. A000071, A191797, A268318. Sequence in context: A089993 A220431 A351284 * A234092 A047931 A258571 Adjacent sequences: A268314 A268315 A268316 * A268318 A268319 A268320 KEYWORD nonn,base,tabf AUTHOR Kival Ngaokrajang, Feb 01 2016 STATUS approved

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Last modified September 30 21:59 EDT 2023. Contains 365812 sequences. (Running on oeis4.)